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Finding the part and finding the whole

Fractions, grade 6 Lesson 10 of 22Learning

Finding the part and finding the whole

Until now you knew the part and the whole quantity, and found the value of the part. Now it goes the other way: you look for the part, or for the whole quantity.

Finding the part

What part of 20 is 4?
Arrange 20 dots in groups of 4:

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There are 5 groups, so 4 is 15\displaystyle \frac{1}{5} of 20. Or straight away: 4 out of 20 is 420=15\displaystyle {\frac{4}{20}}={\frac{1}{5}}.

Comparing parts
Careful: more children does not mean a bigger part of the class – compare the parts.

In grade 6, 5 of the 20 students are scouts; in grade 5, 6 of the 25.
In which grade is a bigger part of the class in the scouts?
Expand both fractions to the denominator 100: grade 6: 520=25100\displaystyle {\frac{5}{20}}={\frac{25}{100}}. Grade 5: 625=24100\displaystyle {\frac{6}{25}}={\frac{24}{100}}. 25100>24100\displaystyle \frac{25}{100}>\frac{24}{100} – grade 6.

Finding the whole

And backwards: 20 students are 45\displaystyle \frac{4}{5} of the class.
How many are in the class?
45\displaystyle \frac{4}{5} are 20 students, so 15\displaystyle \frac{1}{5} is 20÷4=5\displaystyle {20\div4}={5} students, and the whole class – 55\displaystyle \frac{5}{5} – is 5×5=25\displaystyle {5\times5}={25}.

Exercise 1

Find the part: write it as a fraction and reduce.

a
6 out of 18

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b
    15 out of 40

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      Exercise 2

      6 students, who are 15\displaystyle \frac{1}{5} of the class, were absent today.
      How many students are in the class?

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        Exercise 3

        9 is 310\displaystyle \frac{3}{10} of which number?
        Draw a model if it helps.

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power